On the expressive power of temporal logic for finite words

Abstract : We study the expressive power of linear propositional temporal logic interpreted on finite sequences or words. We first give a transparent proof of the fact that a formal language is expressible in this logic if and only if its syntactic semigroup is finite and aperiodic. This gives an effective algorithm to decide whether a given rational language is expressible. Our main result states a similar condition for the "restricted" temporal logic (RTL), obtained by discarding the until operator. A formal language is RTL-expressible if and only if its syntactic semigroup is finite and satisfies a certain simple algebraic condition. This leads to a polynomial time algorithm to check whether the formal language accepted by an n-state deterministic automaton is RTL-expressible.
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Submitted on : Saturday, March 4, 2006 - 4:15:51 PM
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  • HAL Id : hal-00020069, version 1

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Joelle Cohen, Dominique Perrin, Jean-Eric Pin. On the expressive power of temporal logic for finite words. Journal of Computer and System Sciences (JCSS), Elsevier, 1993, 46, pp.271-294. ⟨hal-00020069⟩

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